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研究生： 陳瑋琪
Chen, Wei-Chi
論文名稱： 論不於GF(16)的加法碼
On Additive GF(16) Codes
指導教授： 俞勇
Yu, Yung
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年： 2002
畢業學年度： 90
語文別： 英文
論文頁數： 19
外文關鍵詞： additive GF(16) codes, self-dual
相關次數： 點閱：101  下載：1 
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    Abstract
    In this paper we generalize Gaborit's paper ìOn Additive GF(4) Codesî[2].The additive GF(4) codes are of interest because of their connection to quantum codes [1]. First we de ne the conjugates of nite eld of 16 elements. Next we give the de nition of additive GF(16) codes, the trace map, the trace inner product and their properties, and example of additive GF(16) code. As usual we de ne dual, self-orthogonal, self-dual codes of additive GF(16) codes. Finally, the de nition equivalent codes and automorphism group of additive GF(16) codes are given.

    Contents 1 Introduction 4 2 Finite Field of 16 Elements : GF(16) 4 3 The Conjugates of GF(16) 5 4 Denition of Additive GF(16) Codes 6 5 The Trace Map 6 6 The Trace Inner Product of GF(16) 8 7 Example of Additive GF(16) Codes 11 8 Dual, Self-orthogonal, Self-dual Codes 11 9 Equivalent Codes 18 10 Automorphism Group of Additive GF(16) Codes 18

    References
    [1] A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, "Quantum error correction via codes over GF(4)", IEEE Trans. Inform. Theory IT-44 (1998), 1369-1387.
    [2] P. Gaborit, W. C. Huffman, J-L Kim and V. Pless, "On Additive GF(4) Codes", Appeared in DIMACS Workshop on Codes and Association Schemes, DIMACS Series in Discrete Math. and Theo. Computer Science, A. M. S., Vol. 56 (2001), 135-149.

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